The Steiner problem for infinitely many points (Q624844)
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scientific article; zbMATH DE number 5849494
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Steiner problem for infinitely many points |
scientific article; zbMATH DE number 5849494 |
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The Steiner problem for infinitely many points (English)
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10 February 2011
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Summary: Let \(A\) be a given compact subset of the Euclidean space. We consider the problem of finding a compact connected set \(S\) of minimal one-dimensional Hausdorff measure, among all compact connected sets containing \(A\). We prove that when \(A\) is a finite set any minimizer is a finite tree with straight edges, thus recovering the classical Steiner problem. Analogously, in the case when \(A\) is countable, we prove that every minimizer is a (possibly) countable union of straight segments.
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compact connected set \(S\) of minimal one-dimensional Hausdorff measure
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Steiner problem
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union of straight segments
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